We define the Hopf algebra structure on the Grothendieck group of finitedimensional polynomial representations of Uq ĝlN in the limit N → ∞. The resulting Hopf algebra Rep Uq ĝl∞ is a tensor product of its Hopf subalgebras Repa Uqĝl∞, a ∈ C/q. When q is generic (resp., q is a primitive root of unity of order l), we construct an isomorphism between the Hopf algebra Repa Uq ĝl∞ and the algebra of...

We bosonize certain components of level l Uq(ŝl2)-intertwiners of (l+1)-dimensions. For l = 2, these intertwiners, after certain modification by bosonic vertex operators, are added to the algebra Uq(ŝl2) at level 2 to construct all irreducible highest weight representations of level 1 for the quantum affine algebra Uq(ŝp4).

We define the Hopf algebra structure on the Grothendieck group of finitedimensional polynomial representations of Uq ĝlN in the limit N → ∞. The resulting Hopf algebra Rep Uq ĝl∞ is a tensor product of its Hopf subalgebras Repa Uqĝl∞, a ∈ C/q. When q is generic (resp., q is a primitive root of unity of order l), we construct an isomorphism between the Hopf algebra Repa Uq ĝl∞ and the algebra of...

Let L be the basic (level one vacuum) representation of the affine Kac–Moody Lie algebra ĝ. The m-th space Fm of the PBW filtration on L is a linear span of vectors of the form x1 · · ·xlv0, where l ≤ m, xi ∈ ĝ and v0 is a highest weight vector of L. In this paper we give two descriptions of the associated graded space L with respect to the PBW filtration. The “top-down” description deals with ...

A closed subalgebra of a Banach algebra is called maximal if it is not contained in any larger proper closed subalgebra. Let G be a discrete abelian topological group and L its group-algebra, i.e. L is the Banach algebra of functions/on G with E*e<J |/(X)| < °° and multiplication defined as convolution. What are the maximal subalgebras of L? The complete answer is not known even when G is the g...

In this paper, we establish the Composition-Diamond lemma for associative algebras with multiple linear operators. As applications, we obtain Gröbner-Shirshov bases of free Rota-Baxter algebra, λ-differential algebra and λ-differential Rota-Baxter algebra, respectively. In particular, linear bases of these three free algebras are respectively obtained, which are essentially the same or similar ...

‎For a set of non-negative integers~$L$‎, ‎the $L$-intersection number of a graph is the smallest number~$l$ for which there is an assignment of subsets $A_v subseteq {1,dots‎, ‎l}$ to vertices $v$‎, ‎such that every two vertices $u,v$ are adjacent if and only if $|A_u cap A_v|in L$‎. ‎The bipartite $L$-intersection number is defined similarly when the conditions are considered only for the ver...

In this talk we introduce the notion of a generalized representation of a Jordan algebra with unit which has the following properties: 1) Usual representations and Jacobson representations correspond to special cases of generalized representations. 2) Every simple Jordan algebra has infinitely many nonequivalent generalized representations. 3) There is a one-to-one correspondence between irredu...

Given a (reduced) locally compact quantum group A, we can consider the convolution algebra L(A) (which can be identified as the predual of the von Neumann algebra form of A). It is conjectured that L(A) is operator biprojective if and only if A is compact. The “only if” part always holds, and the “if” part holds for Kac algebras. We show that if the splitting morphism associated with L(A) being...

In this note, we characterize Chebyshev subalgebras of unital JB-algebras. We exhibit that if B is Chebyshev subalgebra of a unital JB-algebra A, then either B is a trivial subalgebra of A or A= H R .l, where H is a Hilbert space